During the return trip from Mars or Moon, SpaceX starship can refuel it's propellant tanks before reentry. It can use these propellants for reverse thrust to bring the spacecraft velocity to near idle velocity before reentry in the Earth atmosphere.

Reentring the Earth's atmosphere with high velocity and using the spacecraft's heatshield alone to reduce the speed and convert the kinetic energy into heat may be suicidal. If refueling of starship in space is a reality, what is the minimum reentry velocity ideal for a spacecraft returning to Earth?

Edited: Idle velocity should not be misconstrued as zero velocity, but the minimum velocity required for safe return of spacecraft to Earth without too much heating in the atmosphere during re-entry. Another concern is chasing the spacecraft by the fuel depot craft for the refueling.

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    $\begingroup$ I wouldn't say relying on the heatshield alone is "suicidal" - Apollo did it just fine $\endgroup$ Apr 18 at 20:03
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    $\begingroup$ @EugeneStyer it was also used by every other spacecraft to ever return to Earth. And on probes to Mars, Venus, Titan, and in one particularly extreme case, Jupiter, where the Galileo atmospheric probe entered at 48 km/s. $\endgroup$ Apr 18 at 21:49
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    $\begingroup$ Seems like you have yet to be introduced to the tyranny of the rocket equation. Pretty much everything can be summed up in, "it will cost an exponential amount of fuel", and the exponential part isn't even a hyperbole, it is a LITERAL exponent. $\endgroup$
    – Aron
    Apr 19 at 10:16
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    $\begingroup$ its propellant tanks. $\endgroup$ Apr 19 at 10:31
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    $\begingroup$ The first lesson of engineering is to not start solving a problem before you're really sure it's actually a problem. $\endgroup$
    – J...
    Apr 19 at 12:53

Your premises are not really correct.

During the return trip from Mars or Moon, SpaceX starship can refuel it's propellant tanks before reentry.

The only way to refuel during the return trip would be for a second Starship to make the same journey from start to finish, alongside the first, at enormous expense.

Reentring the Earth's atmosphere with high velocity and using the spacecraft's heatshield alone to reduce the speed and convert the kinetic energy into heat is suicidal.

There's nothing suicidal about re-entering Earth's atmosphere at high speed. It's been done safely literally hundreds of times before. Only once has a spacecraft's thermal protection system failed to protect a crew (Columbia). Reentry at lunar-return velocity has been done safely nine out of nine times, with enormous safety margins left on the heat shield. Mars return velocity is surprisingly not much different from lunar return. Investing mass in a heat shield and using Earth's atmosphere to decelerate is hugely more efficient than using the same mass in propellant.

Is the idle reentry velocity ideal for a spacecraft returning to Earth?

It's unclear what you mean by idle velocity, but there are dramatic tradeoffs to starting a reentry from speeds significantly lower than orbital. If you reenter by falling straight down, you receive much less total heating, because you get it over with faster, but the crew will receive significantly more peak g-force during the reentry -- depending on the exact design of the spacecraft, this can be over 10-12g, which is hazardous to the crew (and probably beyond the capabilities of the Starship airframe as well). Even in this case, the spacecraft still needs a heat shield of some kind, because it's falling like a hypersonic cannonball through the air. A more gradual reentry from a high horizontal velocity, using aerodynamic lift to bleed off speed and control the rate of descent, takes longer and means the spacecraft has to deal with more total heating, but it's much more comfortable for the passengers; space shuttle crews experienced less than 2g during reentry.

Regardless, Starship was conceived from day one as an interplanetary round-trip spacecraft. It is designed to survive reentry at Martian return speed. (It may have enough fuel margin when taking off from Mars to kill some of its return speed before entering, but I'm fairly certain it'll begin reentry at well over the 8 km/s of low Earth orbit reentries.)

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    $\begingroup$ +1 I suppose that returning from Mars or the Moon they could enter a high and/or very elliptical orbit that a "tanker" from Earth could match. The core of the question to me is "Is there such a thing as an 'ideal velocity' with which to enter Earth's atmosphere?" We can say that 0 km/s is too low and perhaps 20 km/s is way too high, but there's still that problem of defining what "ideal" means. I suppose one could ask for a specific craft like Starship or a refuel-able version of the Shuttle... $\endgroup$
    – uhoh
    Apr 19 at 5:29
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    $\begingroup$ If you can fly the ascent trajectory in reverse, you can get from LEO to surface with no more heat shielding than expendables need on ascent for the same 9400 m/s of delta-v it takes to get from surface to orbit. The TWR is changing in the wrong direction, though, so you might have to start burning earlier and spend more. Unfortunately, Starship is not an SSTO if it's got payload, so it simply can't do it. Unless, of course, you'd like to try to refuel while burning at 3g on a suborbital trajectory. You need a heat shield, so just use the heat shield. $\endgroup$ Apr 19 at 7:18

Ideal required defining the metrics you are using for idealness. From the sound of it, you're thinking about thermal concerns. Obviously reaching roughly 0 velocity in the ECEF frame(0 groundspeed) before reentry will yield the lowest heating. But it has other consequences.

The most obvious is that you have to expend fuel combating gravity. The longer you are in the atmosphere, the more fuel you have to expend. Thus there is an incentive to come down quicker.

Another thing to consider is stability. Descending with a constant nearly-zero velocity is exactly as difficult as it would be for SpaceX to hover one of the boosters above the landing site... for the entire duration of your reentry period! From a dynamics perspective, this can be challenging. Most of our vehicles are designed to move!

If you used these rockets to slow down in the atmosphere, they would have to be pointing "forward," along the velocity vector. Great care would need to be taken to make sure they can stay stable and can withstand the hypersonic winds.

  • $\begingroup$ Lets not forget that it would involve doubling your Delta-V to get to zero velocity again... $\endgroup$
    – Aron
    Apr 19 at 10:17

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